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Research Article
Azimuthally and radially excited charge transfer plasmon and Fano lineshapes in conductive sublayer-mediated nanoassemblies ARASH AHMADIVAND,*
BURAK GERISLIOGLU,
AND
NEZIH PALA
Department of Electrical and Computer Engineering, Florida International University, 10555 W. Flagler St., Miami, Florida 33174, USA *Corresponding author:
[email protected] Received 27 July 2017; revised 5 October 2017; accepted 9 October 2017; posted 9 October 2017 (Doc. ID 303523); published 26 October 2017
Here, the plasmon responses of both symmetric and antisymmetric oligomers on a conductive substrate under linear, azimuthal, and radial polarization excitations are analyzed numerically. By observing charge transfer plasmons under cylindrical vector beam (CVB) illumination for what we believe is the first time, we show that our studies open new horizons to induce significant charge transfer plasmons and antisymmetric Fano resonance lineshapes in metallic substrate-mediated plasmonic nanoclusters under both azimuthal and radial excitation as CVBs. © 2017 Optical Society of America OCIS codes: (250.5403) Plasmonics; (310.5448) Polarization, other optical properties; (310.6805) Theory and design. https://doi.org/10.1364/JOSAA.34.002052
1. INTRODUCTION Interaction of optically driven free electrons across an atomic offset gap spot (d ) between subwavelength plasmonic structures is a quantum mechanical phenomenon that has been characterized by direct quantum tunneling (at d ≤ 0.4 nm) [1,2] and Fowler– Nordheim indirect tunneling principles (at 0.4 ≤ d ≤ 1 nm), with the presence of a high electric field in the gap [3]. Possessing exquisite control over the confined plasmons in the subnanometer gap spot yields an ability to provide on and off states of the induced charge transfer plasmons (CTPs) by varying the intensity of the incident radiation [4], which facilitates reliable platforms for the development of advanced quantum plasmonic nanodevices. To date, astonishing advances have been accomplished in nanofabrication techniques allowing them to reach subnanometer dimensions and anticipate the quantum plasmonic response in nanoscale systems [1–5]. However, these multistep fabrication processes are complex and expensive. Recently, employing much easier and cost-effective methods, CTPs have been induced via bridging the capacitive gap between plasmonic nanoobjects for both nano- and microscale structures to operate across the optical [6,7] to the terahertz [8] frequencies. Besides, Nooshnab et al. [9,10] have shown that the presence of a conductive and functional sublayer below artificial plasmonic oligomers is a simple and effective method to induce CTPs in the visible spectrum. One should note that all of the mentioned progress has been achieved under a classical linear polarization beam (LPB) illumination regime. Lately, researchers have found that incident light with unconventional polarizations [i.e., cylindrical vector beams 1084-7529/17/112052-05 Journal © 2017 Optical Society of America
(CVBs), vortex beams] can be used for excitation of symmetric eigenmodes that cannot be excited by LPB [11,12]. The significance of CVBs, including azimuthal (APB) and radial (RPB) polarized beams, originates from their small focusing spot to excite plasmons as well as facilitating a superior match between the symmetry of the employed nanoantennas and the incident light polarizations [12,13]. Earlier studies have verified that antisymmetric lineshapes such as Fano resonances (FRs) can be excited in both metallic [14–26] and all-dielectric [27–30] nanoparticle (NP) clusters under linear beam illumination. However, excitation of CTPs using CVBs has not yet been analyzed and reported. Here, we study the electromagnetic response of artificial plasmonic molecular clusters in symmetric and antisymmetric geometries that are located on a metallic sublayer with varying thicknesses excited by LPBs and CVBs. Comparing the plasmon responses of both types of clusters, their ability to support Fano lineshapes and CTPs is investigated. Moreover, the effect of their symmetry, incident polarization, and the thickness of the underlying metal layer on the spectral response are discussed and analyzed using a finite-difference time-domain (FDTD) approach and finite element method (FEM) as numerical tools. 2. RESULTS AND DISCUSSION To this end, the seven-member heptamer and eight-member octamer antennas are located on a multilayer substrate consisting of gold and glass (SiO2 ) films. The experimentally obtained Johnson–Christy constants were used for the gold disks as well
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Fig. 1. (a, b) Artistic images for the plasmonic octamer and heptamer on a conductive film layer. (c, d) Normalized scattering cross sections for the plasmonic octamer and heptamer antennas on 5 nm metallic film, respectively, under LPB excitation (plane wave source). The spectral features are indicated by numbers in the profile: (i) dark mode, (ii) Fano dip, (iii) bright mode, and (iv) CTP mode. The inset in (d) shows a cross-sectional image for the thickness of the entire structure (not to scale). (e, f ) Field intensity plots for the FR dips and CTP modes for both antennas.
as for the conductive film in both antennas [31]. Gold disks with a radius and thickness of 125 nm and 60 nm, respectively, are placed apart with an offset gap of 15 nm, for both assemblies, and the radius of the central nanodisk in the octamer was set to 160 nm. The thickness of the underlying gold film is variant, indicated by T Au, and the thickness of the glass sublayer is 400 nm with a relative permittivity of 2.1. To analyze the plasmon response of the structure in the LPB regime, the plasmon hybridization is the major and highly accurate approach [32]. As a basic method, the hybridization mechanism and interference of plasmonic modes in closely packed clusters have been discussed systematically in the literature [33,34]. Figures 1(a) and 1(b) show the artistic images for both antennas on a gold film, with T Au 5 nm under plane wave excitation. In Figs. 1(c) and 1(d), the spectral features are symbolized by “i,” “ii,” “iii,” and “iv,” which correspond to the dark mode, FR dip, bright mode, and CTP mode, respectively. In the linear illumination and non-retarded limits, the dipole moment is close to zero for the subradiant dark mode and cannot efficiently couple with the incident radiation [6,32]. In contrast, in the retarded limit, a destructive coupling between opposite modes gives rise to the formation of a dip between sub- and superradiant modes as a FR dip [34]. According to Sobhani et al. [35], the presence of a metallic sublayer leads to substantial narrowing of the linewidth of the appeared bright mode. This is due to a significant reduction in the corresponding radiative losses of dipolar bright plasmonic mode. Such a narrowness in the bright peak helps to push the FR dip toward the higher energies and produce much sharper asymmetric lineshapes. Notice in Fig. 1(c), for the octamer cluster, a distinct FR dip is induced at 665 nm between narrow dark (530 nm) and broad bright (850 nm) peaks, where a strong peak is induced at 1580 nm correlating with CTP resonance. Technically, this mode is excited due to the ballistic flow of the photoexcited electrons in the offset gaps between proximal NPs at the
low energy levels [9,10]. On the other hand, for the symmetric heptamer, the dark mode remained fixed, while the bright mode is broader than the previous regime and the CTP resonant peak is damped [Fig. 1(d)]. This is because of the inherent symmetry and less complexity of the heptamer antenna. The energy and amplitude of the FR dip is also reduced drastically. Figures 1(e) and 1(f ) exhibit the E-field maps for both antennas, including charge density distribution plots between NPs that are superimposed for the FR and CTP modes. Compared to the metallic clusters on a dielectric layer, the FR dips and bright modes are blue-shifted to the shorter wavelengths, including the presence of a CTP shoulder at lower energies (∼0.7 eV). By changing the polarization of the incident radiation to APB and RPB, we analyze the plasmon responses, as shown in Fig. 2. To this end, generalized multiparticle Mie theory for spherical NPs can be used [21], where the incident, internal, and scattered fields are included in the calculations. Assuming harmonic time dependence as exp−iωt, the E-field relation for mth NP in an assembly with a standard boundary condition is given by [14,36] E inc m E scat m − E int m × nm r 0:
(1)
This principle was proposed to expand all of the contributed fields in vector spherical harmonics to extract the plasmon response analytically by using proper perfectly matched layers (PMLs) as boundary conditions. Therefore, the scattered field can be rewritten as a function of spherical harmonics (A) and (B) defined by Gérardy and Ausloos [37] with Bessel function spherical harmonics (ij3 ): E scat m; r
∞ X i X
m am ij Aij3 m; r bij B ij3 m; r:
(2)
i1 j−i
Figure 2(a) shows the extinguished power profile as a function of the incident beam for the octamer antenna under APB and RPB radiations. Here, the middle NP does not support
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Fig. 2. Extinguished power spectra for plasmonic (a) octamer and (c) heptamer clusters under both APB and RPB illuminations. (b, d) E-field maps for the Fano dip, dark mode, and CTP resonant modes in octamer and heptamer clusters, respectively. (e, f ) Charge density maps for the Fano and CTP modes under APB illumination for octamer and heptamer clusters, respectively.
a significant dipolar moment under both CVBs. In this regime, under APB exposure, we observed a FR dip in the extinguished power spectra. Theoretically, each NP holds a net dipolar moment and couples the moment to the proximal particles. In the FR wavelength, due to asymmetric orientation of peripheral NPs, a collective mode is induced with an opposite phase to the incident light phase, leading to the formation of a destructive interference of the modes. Excitation of the plasmonic modes leads to the substantially large field enhancement that is observed as hotspots in the offset gaps of the peripheral nanodisks. In contrast, in the RPB limit, both dark and FR modes are damped dramatically. This is due to the absence of the required group antisymmetry and the lack of efficient localization of plasmons and coupling of excited modes between proximal NPs. One should note that the bright mode is induced due to efficient coupling to the incident light, and the combination of plasmonic resonant modes with the same symmetry with inphase polarizations is responsible for the bright mode excitation under CVB radiation [27]. In addition, we observed notable shoulders corresponding to the CTP resonance around ∼1600 nm at the lower energies for both APB and RPB due to the redistribution of the charges via thin gold film to NPs. However, this mode also damped slightly, since dipolar bright and multipolar dark modes in a single NP are split into a cluster, resulting in lower energy. Despite this decay in the energy of the CTP resonant mode, we observed, for what we believe is the very first time, CTPs under CVB radiation. Figure 2(b) demonstrates the E-field maps for each feature with arrows that show the localization and transition of charges under CVB illumination.
Using the same strategy, we studied the electromagnetic response of the heptamer antenna. In this case, due to the symmetry of the assembly, we expect a dramatic decay in the quality of the subradiant dark mode, as discussed in [13]. In the absence of a dipole moment in the central disk, however, in contrast to the octamer assembly, there is no observed significant antibonding shoulder in the scattering profile, as shown in Fig. 2(c). In this regime for the APB, a very weak shoulder correlating with subradiant dark mode is detected; for the RPB radiation, however, the dark mode is damped entirely. The bright modes for both polarizations became dominant (around 600 nm), while the Fano-like dip vanished and just a shoulder correlating with the CTP peak appeared around 1580 nm. Notice the plotted charge distribution profiles for the APB, where strong hotspots formed between peripheral disks due to electron–electron interference between the excited charges in the thin underlying film and the NPs, while the central disk does not have a net dipolar moment [Fig. 2(d)]. For the RPB, the proximal NPs possess a dipolar moment in the outward direction and are repelling each other. In contrast to the APB, coldspots are formed for the RPB between the neighboring NPs. In this regime, hotspots are formed between the surrounding NPs and the central one due to the effect of the underlying conductive layer and dipolar moments within the disks, as we discussed earlier. In addition to the broad dipolar mode, the redistribution of charges also led to an arising CTP feature at low energies (∼0.69 eV). Specifically, for the heptamer under APB excitation [Fig. 2(d)], hotspots are also formed between the surrounding NPs and the middle disk. These energetic areas are created due to the interference of
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Fig. 3. Extinguished power spectra for the octamer antenna for variant sublayer thickness under (a) LPB, (b) APB, and (c) RPB excitations.
low-energy multipolar modes and energetic dipolar modes supported by the conductive sublayer, leading to the formation of a CTP extreme. In this case, the intensity of the charge travel in the octamer cluster is much more than the one in the heptamer assembly. Figures 2(e) and 2(f ) illustrate the charge density maps obtained by the FEM tool for the position of Fano and CTP modes under APB illumination for octamer and heptamer assemblies, respectively. In all of the examined regimes, the thickness of the conductive substrate was very thin and fixed to 5 nm. However, this layer has a noteworthy contribution in the excitation of CTPs and the enhancement of the Fano lineshape (Fig. 3). Focusing on the octamer cluster, by increasing T Au , both dark and bright modes are damped due to increased absorption at these energy states (dissipative losses). This dampingis reflected in the profile by broadening of the bright mode and by reducing the intensity of the dark mode. The significant result of this damping is losing the Fano minimum. In addition, the CTP peak is red-shifted to very low energies for all incident polarizations [Figs. 3(b) and 3(c)]. Ultimately, we plotted the CTP mode and FR dip energy dependence on the conductive layer thickness as shown in Figs. 4(a) and 4(b). For Fano dip energies [see Figs. 4(a) and 4(b)], increasing T Au led to a blue-shift of the minimum to the higher energies for all polarizations, where the energy difference and corresponding shift is significant in the CVB regime. Figures 4(c) and 4(d) illustrate the CTP energy variations as a function of T Au . By increasing the conductive layer thickness, the CTP shoulder is red-shifted to the smaller energies. In the latest analysis, the shift of the resonances for CVB and LPB regimes is almost in the same route for the octamer antenna (Fig. 4). Numerical analysis was performed using the threedimensional FDTD method (Lumerical 2017) and FEM (COMSOL Multiphysics 5.2). The workplace is surrounded with perfectly matched layers (PMLs) as boundaries with the number of 64, and a spatial grid size of Δx Δy Δz 1 nm for meshing the structure. To define the magnetic surface’s current plot, a divergence current module was applied to the FDTD model. The charge density plots were obtained by applying an RF module and implementing Gauss’s theorem across the surface of the nanostructures. For linear illumination,
Fig. 4. (a) Fano dip and (b) CTP resonance energies as a function of conductive film thickness for octamer cluster under three different polarized beam illuminations.
a classical plane wave was employed and the CVB illumination regimes were obtained by applying the corresponding codes in the FDTD solutions [38]. 3. CONCLUSIONS In summary, we have reported numerical studies of the optical and plasmonic properties of azimuthally and radially excited symmetric and antisymmetric complex NP clusters placed
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on a thin metallic film. Our analysis has shown that the proposed nanostructures can be tailored to support strong dark modes and CTPs under CVB polarizations. In addition, the effects of symmetry and the conductive film thickness are discussed, and the energy of CTPs has been compared for different polarizations. Funding. Army Research Laboratory (ARL) (W911NF-122-0023); Multiscale Multidisciplinary Modeling of Electronic Materials (MSME); Collaborative Research Alliance (CRA). Acknowledgment. Arash Ahmadivand gratefully acknowledges the financial support provided through a doctoral evidence acquisition (DEA) fellowship by the University Graduate School (UGS) at Florida International University.
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